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Math Help - why am i blanking so hardcore? -stats

  1. #1
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    why am i blanking so hardcore? -stats

    let X(bar) be the mean of a random sample of size n=10 from a distribution with pdf f(x) = 6x(1-x) for 0<x<1. Find the mean and the variance of X(bar).

    I feel like there is just a simple formula for this but I cannot for the life of me remember this. It sounds like a foreign language right now! Please help with any input you can, this is due tomorrow.
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  2. #2
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    Quote Originally Posted by Dubulus View Post
    let X(bar) be the mean of a random sample of size n=10 from a distribution with pdf f(x) = 6x(1-x) for 0<x<1. Find the mean and the variance of X(bar).

    I feel like there is just a simple formula for this but I cannot for the life of me remember this. It sounds like a foreign language right now! Please help with any input you can, this is due tomorrow.
    \overline{x} = \frac{X_1 + X_2 + \, .... \, + X_9 + X_{10}}{10}

    \Rightarrow E(\overline{x}) = E\left( \frac{X_1 + X_2 + \, .... \, + X_9 + X_{10}}{10}\right)  = \frac{E(X_1) + E(X_2) + \, .... \, + E(X_9) + E(X_{10})}{10} = E(X).

    And you calculate E(X) from the given pdf of X.

    Use the same approach to find E\left(\overline{x}^2\right). Then get Var(\overline{x}) in the usual way.
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  3. #3
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    wont we divide by (n-1) which is 9 in this case? (something to do with degrees of freedom cos this is a sample that we need)
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    Quote Originally Posted by champrock View Post
    wont we divide by (n-1) which is 9 in this case? (something to do with degrees of freedom cos this is a sample that we need)
    When you find a mean of a sample you divide by the sample size. Unless you know something about this question that you're not telling anyone ....
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